Calculate the amount of money that will be in each of the following
accounts at the end of the given deposit period:

Account

Amount
Deposited

Annual
Interest Rate

Compounded
Every..... Months

Deposit
Period (years)

Brown

$
1,000

10%

12

10

Coles

95,000

12

1

1

Elliott

8,000

12

2

2

Robinson

120,000

8

3

2

Chin

30,000

10

6

4

Daley

15,000

12

4

3

At what annual rate would the following have to be invested?

(a)
$500 to grow to $1,948.00 in 12 years

(b) $300
to grow to $422.10 in 7 years

(
c) $50
to grow to $280.20 in 20 years

6-10

How
many
years will the following take:

(a)$40 to grow
to S88.44 if invested at 12% compounded annually?

(b)
$110 to grow to
$614.79 if invested at 24% compounded annually?

(c)$550
to grow to $1,043.90 if invested at 6% compounded annually?

6-3

What is the value of $50,000 at the end of three years from today if it
earns 20% per annum:

(a)
interest
paid continuously

(b)
interest paid daily

(c)
interest paid each quarter

(d)
interest
paid semiannually

(e)
interest paid every 18 months

If you were to quit
UTech at the end of this semester and deposit your
next semester’s tuition of $32,000 in
an account paying 20% per annum
compounding daily. What effective annual interest rate would you earn? What
would be the balance in the account in three years?

A local credit card company purports to charge an annual percentage rate
of 5.5% per
month, a total of 66% per annum. Is
this a correct claim? Explain.

6-5

You are planning to deposit $10,000 today in a bank account. Five years
from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account nine years
from today?

You
have just graduated and you plan to
work for 8 years and then leave for Canada. You figure you can
save $5,000 a year for 5 years
and $2,500 a year for the last three years. The cash flows will start one year
from now. In addition, your grandfather has just given you a $10,000 graduation
gift.

If
you put this gift and your future savings in an account paying 10% compounded
annually, what will be the amount you will have when you leave for Canada 8
years hence?

You
would like to start your own retirement plan now by making a deposit of $25,000
each year in a bank account which will earn 10% interest compounded annually.
Your first payment will be made at the end of the year for 20 years at the end
of which you will retire. At the end of year 21 you will deposit $35,000 to the
account and then $45,000, $60,000 and $25,000 in the following years (years 22
to 24) representing gratuity payments from your company.

At the end of year 25 when you are ready to begin withdrawing funds from
the account what will be its balance?

6-14

6-24

6-26

6-43 (The third line in part C should read
"101.60" and not "101.75" )

6-20

Present Value

6-2

What is the lump sum you would have to deposit now in order to have the
balance at question 13. (above) in the account in 25 years?

6-42

Find the present value of the following cash flow stream, discounted at
5% per annum:

Year 1$1,000Year 2$4,000Year3—20$3,000

(a)assume the cash flows occur at the end of each year

(b)assume the cash flows occur at the beginning of each year

Find the present value of an income stream that has a negative flow of
$100 per year for the first three years, a positive flow of $200 in the fourth
year and a positive
flow of $300 in years five through eight. The appropriate discount rate is 4%
for each of the first three years and 5% for
each of the later years.

Your father has just inherited a large sum of money and he would like to
know how much to save for retirement and how much he can spend now.

For
retirement he will deposit a lump sum in an account today (January 1, 2001) and
will earn 10% compounded annually. He does not intend to use this money until he
retires in 5 years (January 1, 2006), and he assumes he will live for 20
additional years after which he thinks he will die on December 31, 2025.

During
his retirement he would like to receive income of $60,000 per year to be
received the first day
of each year, with the first payment on January 1, 2006, and the last payment on
January 1,2025.

Complicating
this objective, however, is his desire to have one final three-year African tour.
To finance this he wants to receive $300,000 on January 1, 2021, (instead of the
usual S60,000), and nothing on January 1, 2022, and January 1, 2023, as he will
be on tour. In addition, after he dies (January 1, 2026), he wants to leave
$100,000 in his account for you.

How
much must he deposit in his account at 10% on January 1, 2001 in order to
achieve this goal?

6-25

Perpetuity

6-16

Loan
Amortization

You
borrow $10,000 at 10% for 5 years. The
loan is payable in five equal installments at the beginning of each year.

(a)What is the annual payment
that will completely amortize the loan over 5
years?

(b)Construct an amortization
schedule to show the amount of interest and
the amount of principal paid each
year.

The loan officer of your building society has told you that the interest
rate on home loans is 24% per annum for a period of 40 years. Interest is
charged monthly on the loan.

(a)What is the effective annual interest rate on the loan?

(b)Find the monthly payment on a $300,000 loan. (assuming that payments are
made at month end)

(c)Prepare an amortization table for the first four months.

(d)Compute the loan balance just after the end of year 35.

6-19

You took a loan from a bank under the following terms: $150,000 on a
reducing balance basis,
requiring you to pay $9,838.07 at the end of each month over the next 24 months.

(a)What is the monthly interest rate?

(b)What is the annual nominal interest rate?

(c)What is the annual effective interest rate?

6-12

6-9

6-45

Comprehensive
questions

6-22

6-47

Segma
Investment Inc. wishes to accumulate funds to provide a retirement annuity for
the Vice President of Marketing, Jill Morgan. By contract, Jill will retire
exactly 12 years from now. One year after retirement she is entitled to receive
an annual payment of $42,000
for exactly 20 years. If she dies before the end of the 20-year period, the
annual payments will pass to her heirs.

During
the 12-year “accumulation period,” Segma wishes to fund the retirement
annuity by making equal annual end of year deposits into an account earning 9%
interest. Once the 20-year “distribution period” begins, Segma plans to move
the accumulated monies into an account earning a guaranteed 12% per year.

(a)How large a sum must Segma Investments accumulate by the end of year 12
to provide the 20-year, $42,000 annuity?

(b)
How large must Segma’s equal annual end of year deposits into the account be
over the 12-year accumulation period to fully fund Jill’s retirement annuity?

(c)How much would Segma have to deposit annually during the accumulated
period if Jill’s retirement annuity was a perpetuity and all other terms were
the same as initially described?